Spartacus, a 15-year-old carriage horse, fell onto his side Wednesday afternoon across from the Plaza Hotel, becoming the latest flashpoint in the debate over the Central Park horses. Mr. de Blasio has said he will make good on a campaign promise to ban the horses over the concerns of animal rights groups who say the four-legged animals have no place in busy Midtown traffic.

“Look, every time we talk about this issue I say I have seen so many of these accidents,” the mayor said at an unrelated news conference Thursday.

“A horse is not supposed to be right next to a bus in the middle of the biggest city in the country.”

Mr. de Blasio was echoing animal rights activists who said the horse was spooked by a bus; carriage drivers said that was untrue, and said the horse simply lost his balance after his carriage became tangled with that of another carriage horse.

“He did not spook. He did not collapse,” said Christina Hansen, a carriage driver and a spokeswoman for the carriage drivers. “He was not startled by a bus.”

Ms. Hansen said Spartacus was unharmed and “behaved like a gentleman,” remaining calm as he was helped back to his feet before being led back to the stables, where he was seen by a veterinarian.

Video of the horse lying on the ground was captured by a tourist and circulated by groups like People for the Ethical Treatment of Animals, or PETA, and New Yorkers for Clean, Livable and Safe Streets, or NYCLASS, which supports a ban and backed Mr. de Blasio’s campaign for mayor. On Thursday, NYCLASS held a protest to condemn the horse carriages at the scene of the accident.

The union that represents the city’s carriage drivers organized its own event in response to the accident Thursday, inviting the media to visit Spartacus at his West Side stables. Alex Moore, a spokesman for the union, the Teamsters Local 553, said the horse had been given a “clean bill of health” from his veterinarian, and promised to have the documentation on hand.